Are Government Bonds Net Wealth?
Robert J. Barro
University of Chicago
‘The assumption that government bonds are perceived as net wealth by
the private sector is crucial in demonstrating real effects of shifts in the
stock of public debt. In particular, the standard effects of “expansionary”
fiscal policy on aggregate demand hinge on this assumption. Government
bonds will be perceived as net wealth only if their value exceeds the cap-
italized value of the implied stream of future tax liabilities. This paper
considers the effects on bond values and tax capitalization of finite
lives, imperfect private capital markets, a government monopoly in the
production of bond “liquidity services,” and uncertainty about future
tax obligations. It is shown within the context of an overlapping-
generations model that finite lives will not be relevant to the capitaliza-
tion of future tax liabilities so long as current generations are
connected to future generations by a chain of operative intergenerational
transfers (either in the direction from old to young or in the direction
from young to old). Applications of this result to social’ security and
to other types of imposed intergenerational transfer schemes are also
noted. In the presence of imperfect private capital markets, government
debt issue will increase net wealth if the government is more efficient,
at the margin, than the private market in carrying out the loan process.
Similarly, if the government has monopoly power in the production
of bond “liquidity services,” then public debt issue will raise net wealth.
Finally, the existence of uncertainty with respect to individual future
tax liabilities implies that public debt issue may increase the overall
risk contained in household balance sheets and thereby effectively re-
duce household wealth.
The assumption that government bonds are perceived as net wealth by
the private sector plays an important role in theoretical analyses of
monetary and fiscal effects. This assumption appears, explicitly or im-
plicitly, in demonstrating real effects of a shift in the stock of public debt
I have benefited from comments on earlier drafts by Gary Becker, Benjamin Eden,
Milton Friedman, Merton Miller, José Scheinkman, Jeremy Siegel, and Charles Upton.
‘The National Science Foundation has supported this research.
(Journal of Pais! Economy, 1974, vol 82, n0. 6)
O°1874 by The University of Chicago. All rights reserved
10951096 JOURNAL OF POLITICAL ECONOMY
(see, e.g., Modigliani 1961, sec. IV; Mundell 1971; and Tobin 1971,
chap. 5), and in establishing nonneutrality of changes in the stock of
money (Metzler 1951, sec. VI). More generally, the assumption that
government debt issue leads, at least in part, to an increase in the typical
household’s conception of its net wealth is crucial for demonstrating a
positive effect on aggregate demand of “expansionary” fiscal policy, which
is defined here as a substitution of debt for tax finance for a given level of
government expenditure (see, e.g., Patinkin 1964, sec. XII.4; and Blinder
and Solow 1973, pp. 324-25). The basic type of argument in a full-
employment model is, following Modigliani (1961), that an increase in
government debt implies an increase in perceived household wealth;
hence, an increase in desired consumption (a component of aggregate
demand) relative to saving; hence, an increase in interest rates; and,
finally, a decline in the fraction of output which goes to capital accumula-
tion. However, this line of reasoning hinges on the assumption that the
increase in government debt leads to an increase in perceived household
wealth. In a non-full employment context it remains true that the effect of
public debt issue on aggregate demand (and, hence, on output and
employment) hinges on the assumed increase in perceived household wealth.
It has been recognized for some time that the future taxes needed to
finance government interest payments would imply an offset to the direct
positive wealth effect. For example, in a paper originally published in
1952, Tobin (1971, p. 91) notes: “How is it possible that society merely
by the device of incurring a debt to itself can deceive itself into believing
that it is wealthier? Do not the additional taxes which are necessary to
carry the interest charges reduce the value of other components of private
wealth?” Bailey (1962, pp. 75-77) has gone somewhat further by arguing:
“It is possible that households regard deficit financing as equivalent to
taxation. The issue of a bond by the government to finance expenditures
involves a liability for future interest payments and possible ultimate
repayment of principal, and thus implies future taxes that would not be
necessary if the expenditures were financed by current taxation. ... If
future tax liabilities implicit in deficit financing are accurately foreseen,
the level at which total tax receipts are set is immaterial; the behavior of
the community will be exactly the same as if the budget were continuously
balanced.”
‘There seem to be two major lines of argument that have been offered
to defend the position that the offset of the future tax liabilities will be
only partial.! One type of argument, based on finite lives, supposes that
+ Of course, most analyses of government debt effects do not offer a specific defense
for this position. For example, Blinder and Solow (1973, p. 325, n. 8) say: “This [analysis]
includes government bonds as a net asset to the public. We are well aware of, but not
persuaded by, the arguments which hold that such bonds are not seen as net worth by
individuals because of the implied future tax liability.”GOVERNMENT BONDS 1097
the relevant horizon for the future taxes (which might correspond to the
remaining average lifetimes of the current taxpayers) will be shorter than
that for the interest payments.” Accordingly, a stream of equal values for
interest payments and taxes will have a net positive present value. This
argument has been used explicitly by Thompson (1967, p. 1200). The
second type of argument, usually based on imperfect private capital
markets, supposes that the relevant discount rate for tax liabilities will
be higher than that for the interest payments. Hence, even with an infinite
horizon for tax liabilities, a stream of equal values for interest payments
and taxes will have a net positive present value. This argument has been
used by Mundell (1971).?
‘The first part of this paper deals with the effect of government bond
issue on the calculus of individual wealth in an overlapping-generations
economy with physical capital where individuals have finite lives. No
elements of “capital market imperfections” are introduced into this model.
‘The key result here is that, so long as there is an operative intergenerational
transfer (in the sense of an interior solution for the amount of bequest or
gift across generations), there will be no net-wealth effect and, hence, no
effect on aggregate demand or on interest rates of a marginal change in
government debt. This result does not hinge on current generations’
weighing the consumption or utility of future generations in any sense on
an equal basis with own consumption, nor does it depend on current
generations’ placing any direct weight at all on the consumption or utility
of any future generation other than the immediate descendant. Current
generations act effectively as though they were infinite-lived when they
are connected to future generations by a chain of operative inter-
generational transfers.
The analysis then shows that social security payments are analogous to.
changes in government debt. Marginal changes in this type (or other
types) of imposed intergenerational transfers have no real effects when
current and future generations are already connected by a chain of opera-
tive discretionary transfers. The effects of inheritance taxes and of
“transaction costs” for government bond issue and tax collections are also
considered. It is shown that inheritance taxes do not affect the basic
results, but that the presence of government transaction costs implies that
the net-wealth effect of government bonds would actually be negative.
The second part of the paper deals with the existence of imperfect
private capital markets. It is shown that, to the extent that public debt
2 This type of argument applies to head taxes or to taxes based on wage income, but
not to taxes which are based on the value of nonhuman assets. This distinction has been
made by Mundell (1971, pp. 9, 10).
> AA different line of argument that leads to a similar conclusion is that the government
acts like a monopolist in the provision of the liquidity services yielded by its liabilities.
I discuss this argument in part IIT, below.1098 JOURNAL OF POLITICAL ECONOMY
issue entails a loan from low-discount-rate to high-discount-rate individ-
uals, a positive net-wealth effect results if the government is more efficient
than the private market in carrying out this sort of loan. If the government
is more efficient only over a certain range, and if the public choice process.
determines the amount of government debt issue in accord with efficiency
criteria, it is again true at the margin that the net-wealth effect of
government bond issue is nil.
The third part of the paper discusses government debt as a bearer of
nonpecuniary “liquidity services.” It is shown that if the government acts
like a competitive producer of these services, as would be dictated by a
public choice process which reflects efficiency criteria, then the net-
wealth effect of government bond issue would be zero on this count. More
generally, the net-wealth effect would be positive if the government acts
like a monopolist and would be negative if the government is an
overproducer of liquidity services.
‘The last part of the paper deals with the risk characteristics of govern-
ment debt and of the tax liabilities associated with the interest payments
on this debt. It is argued that if relative tax liabilities are known, a change
in government debt will not alter the overall risk contained in household
balance sheets. When relative tax liabilities are uncertain, the effect of
government debt issue on the overall risk may be positive or negative,
depending on the nature of the tax system and on the transaction costs
associated with private insurance arrangements.
I. The Effect of Finite Lives—a Model with Overlapping Gener-
ation
A. Setup of the Model
I use here a version of the Samuelson (1958)-Diamond (1965) over-
lapping-generations model with physical capital. Each individual lives
two periods, which will be distinguished by the superscripts » (young)
and o (old). Generations are numbered consecutively beginning with the
generation which is currently old (subscript 1) ; followed by its descendant,
which is currently young (subscript 2); followed by its descendant; and
so on. I assume here that there are the same number of people, N, in each
generation, and that all individuals are identical in terms of tastes and
productivity. I also abstract from any technological change over time.
‘The members of each generation work (a fixed amount of time set equal
to one unit) only while young and receive an amount of wage income w.
Expectations on w for future periods (i.c., for future generations) are
assumed to be static at the current value, Asset holdings (A) take the form
of equity capital (K). Subsequently, government bonds are introduced as
an additional form in which assets can be held. The rate of return on assetsGOVERNMENT BONDS 1099
is denoted by r and is assumed to be paid out once per period. Expectations
on r for future periods are assumed to be static at the current value. A
member of the ith generation holds the amount of assets 4? while young
and the amount 4j while old. The asset holding while old constitutes the
provision of a bequest, which is assumed to go to the immediate descen-
dant, a member of generation i + 1. Since the focus of the analysis
concerns shifts in tax liabilities and government debt for a given level of
government expenditure, it is assumed for convenience that the govern-
ment neither demands commodities nor provides public services. In this
section, it is also assumed that the amounts of government debt and taxes
are zero. Using the letter ¢ to denote consumption, and assuming that
consumption and receipt of interest income both occur at the start of the
period, the budget equation for a member of generation 1, who is currently
old, is
Al + Ag = 2 + (1 — 1)AB. ay
The total resources available are the assets held while young, A?, plus the
bequest from the previous generation, Ag. The total expenditure is con-
sumption while old, cf, plus the bequest provision, A’, which goes to a
member of generation 2, less interest earnings at rate r on this asset
holding.
‘The budget equation for members of generation 2 (and, more generally,
for members of any generation i > 2) is, assuming that wage payments
occur at the start of the young period,
w = + (1 — 1)A2, (2)
and, for the old period,
AS + AS = 8 + (1 — 1) AB. (3)
A portion of the lifetime resources of a member of generation i goes to a
bequest provision, A?, which I assume is motivated by a concern for a
member of generation i + 1. This concern could be modeled by intro-
ducing either the (anticipated) consumption levels or attainable utility
of a member of generation i + 1 into the utility function for a member of
the ith generation. For the purpose of the present analysis, the crucial
condition is that this utility depend on the endowment of a member of
generation i + 1 rather than, per se, on the gross bequest, 4°. (The
distinction between the gross bequest and the net bequest, which deter-
mines the endowment of i + 1, will be discussed below.) So long as a
member of generation i can transfer resources to a member of generation
i + 1 only through the transfer of unrestricted purchasing power (which
rules out the “merit good” case discussed in n. 8 below), the two types of
models of interdependent preferences—concern with consumption levels
and concern with attainable utility—will be equivalent in the sense of1100 JOURNAL OF POLITICAL ECONOMY
indirectly implying a concern for the endowment of a member of
generation i + 1.
For present purposes, it is convenient to assume that the utility of a
member of generation i depends solely on own two-period consumption,
c? and cf, and on the attainable utility of his immediate descendant, Us, .
The asterisk denotes the maximum value of utility, conditional on given
values of endowment and prices. Hence, the utility function for a member
of the ith generation has the form,*
U.
Ue, ey UR) (4)
Subsequently, I consider the implications of entering the attainable
utility of a member of the previous generation, U;*,, as an additional
argument of the U; function.
Each member of generation 1 determines his allocation of resources
to maximize U,, subject to equations (1)-(4) and to the inequality
conditions, (ci, c?, 4%) > 0 for all i. The key restriction here is that the
bequest to the member of the next generation cannot be negative. The
choice of bequest, subject to this restriction, takes into account the effect
of A? on generation 2’s resources, the impact of US on U,, and the chain
dependence of U on U¥, of U; on Uf, etc. The solution to this problem
will take the general form
ef = oy(At + AG, w, 1),
i 6)
At = (At + AS ~ of) = AUAY + 48, , 7)
Similarly, for members of generation 2 (and, more generally, for members
of any generation i > 2), the solution would take the form,
3 = 03(Aj, w, 1),
1
l-r
(w — 3) = A3(AR, w, 7),
(6)
2 = 03(A} + AP, w, 7),
(Ad + AY — 03) = A3(A3 + Aj, w, 1).
l-r
* A member of generation i is assumed to be concerned with own consumption and
with the attainable indifference surface of his descendant. Further, it is supposed that a
member of generation i can attach a metric to generation i + 1’s indifference surface
which makes it comparable to c? and cf in terms of generating U; in the form of eq. (4).
‘The nature of this sort of utility function is discussed in the general context of inter-
dependent preferences in Becker (1974, sec. 3.A).
51 have not imposed the condition, 47 > 0, so that young individuals are allowed
to issue interest-bearing debt on themselves. If issued, these debts are assumed to be perfect
substitutes for equity capital. These debts correspond to the consumption loans which
have been discussed by Samuelson (1958).GOVERNMENT BONDS 1101
The model can be closed, as in Diamond (1965, pp. 1130-35), by
specifying a constant-returns-to-scale production function that depends
on the amounts of capital and labor input, and by equating the marginal
products of capital and labor to r and w, respectively. The value of r for
the current period would then be determined in order to equate the
supply of assets to the demand—that is,
K(r, w) = At + A}, (eg)
where K(r, w) is such as to equate the marginal product of capital to r.
The current demand for assets, A? + A}, depends, from equations (5)
and (6), on r, w, and the previous period’s value of K, which is equal to
A} + A§. Since the number of people in each generation is assumed to
equal a fixed number N,, it is not necessary to enter this number explicitly
into the aggregate asset demand in equation (7). Similarly, N is omitted
from the aggregate formulations below. Since N is constant and technical
change is not considered, the current and previous periods’ values of K
would be equal in a steady state.
With the marginal product of labor equated to w and with constant
returns to scale, output is given by
p=rK+w. (8)
Equations (2), (3), (7), and (8) imply a commodity market clearing
condition,
t+ ch + AK = y, (9)
where AK denotes the change in capital stock from the previous to the
current period. The value of AK would be zero in a steady state, but the
present analysis is not restricted to steady-state situations.
B. Government Debt
Suppose now that the government issues an amount of debt, B, which can
be thought of as taking the form of one-period, real-valued bonds. These
bonds pay the specified amount of real interest, rB, in the current
period and the specified real principal, B, in the next period.® It is
supposed that asset holders regard equity and government bonds as
perfect substitutes. It can be assumed, for simplicity, that the government
bond issue takes the form of a helicopter drop to currently old (generation
1) households. Equivalently, it could be assumed that the bonds were
sold on a competitive capital market, with the proceeds from this sale
used to effect a lump-sum transfer payment to generation 1 households.
The amount of bond issue would be limited by the government’s collateral, in the
sense of its taxing capacity to finance the interest and principal payments (see n. 12
below).